with periodic boundary conditions on a domain of size \(L=22\) . Solutions are found by performing a Galerkin projection onto Fourier modes and using exponential time differencing to evolve the ODE forward in time [1]}. After solving in Fourier space, we then transform the data back to physical space for training the neural ODEs. Code for solving the KSE is available in Cvitanović et al. [2]}. The data used is a single trajectory that has collapsed onto the inertial manifold evolved over \(t=[0,10^5]\)  sampled every \(0.25\)  time units. The first 80% of this data is used for training and the remaining 20% is used as test data.
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